Classification and compression are common operations in image processing. Conventionally, compression and classification algorithms are independent of each other and performed sequentially. In this paper, a new algorithm is developed, where the two operations are combined in order to optimize some given classification metrics. In other words, the compression ratio is maximized under classification constraints. Compression is achieved using Adaptive Differential Pulse Code Modulation (ADPCM), which has an adaptive predictor. The predictor coefficients are updated in real-time by optimizing a cost function based on classification metrics. Optimization is done using a simple genetic algorithm. Computer simulations are performed on hyperspectral images. The results are promising and illustrate the performance of the algorithm under various constraints and compression schemes. Keywords—GA-ADPCM, SOM, compression, classification

In this paper, a novel approach is presented for designing multiplier-free state-space digital filters. The multiplier-free design is obtained by finding power-of-2 coefficients and also quantizing the state variables to power-of-2 numbers. Expressions for the noise variance are derived for the quantized state vector and the output of the filter. A "structure-transformation matrix" is incorporated in these expressions. It is shown that quantization effects can be minimized by properly designing the structure-transformation matrix. Simulation results are very promising and illustrate the design algorithm.

This paper presents a unified framework for adaptive filters based on a line search method. Expressions for this unified framework are derived. Based on this framework new algorithms are derived, namely, diagonal Q-correlation matrix least square algorithm (DQLS), block diagonal Q-correlation matrix least square algorithm (BDQLS) and their reduced complexity variants. It is shown that both DQLS and BDQLS have less computational complexity compared to EDS and RLS, and better performance than LMS.

In this paper, we propose an adaptive algorithm for blind identification of single-input multiple-output (SIMO) systems. The algorithm consists of p−1 parallel recursive estimators, where p is the number of system outputs. We analyze the normalized least-mean square (NLMS) estimator, and the weighted recursive least-squares (WRLS) algorithm. It is proved that parameter estimates converge toward a scalar multiple of the true parameters with probability one. The value of the scaling factor is calculated. Numerically simple p−1 parallel NLMS recursions are potential candidate for real-time blind identification applications.

In this paper, a transient analysis is performed for a least squares based adaptive algorithm, Euclidean direction search algorithm. The transient analysis is characterized by derivations of the energy conservation relation and the learning curve equation. The learning curve equation is particularly important because it describes the learning mechanism of the algorithm without an explicit recursion for the weight vector.

This work presents a method for resolving the directions of arrival in both the azimuthal and elevation plane simultaneously using a planar array. An adaptive algorithm, based on Pisarenko's harmonic retrieval method, is presented and implemented.

This paper is based on a recently published class of adaptive filtering algorithms, namely, the Euclidean direction search (EDS) algorithms. The computationally efficient version is called the fast Euclidean direction search (FEDS) algorithm with a computational complexity of O(N). In this paper, we present two new algorithms called the optimal Euclidean direction search (OEDS) and the optimal fast Euclidean direction search (OFEDS). The optimal algorithms search all the Euclidean directions in each iteration to find the direction giving the greatest decrease of the cost function. In order to reduce the computational complexity, some sub-optimal methods based on the same principle are also discussed. Computer simulation results illustrate that the optimal and suboptimal algorithms converge faster than the original EDS and FEDS algorithms, but achieve the same steady state mean square error.

The paper develops an extension of the adaptive RLS-type algorithm proposed by X.-L. Zhu and X.-D. Zhang (see IEEE Sig. Process. Lett., vol.9, no.12, p.432-5, 2002). Their work uses the matrix inversion lemma to solve iteratively the equation obtained from the natural gradient of the nonlinear principle component analysis problem. We reduce the complexity of the solution by applying the Euclidean direction search concept in place of the matrix inversion lemma. The simulations performed show that the convergence rate is comparable, albeit slower, but with reduced complexity per iteration.

This paper proposes a fast algorithm for computing the approximated DFT, called the Fast Integer Fourier Transform (FIFT). The new transform is based on factorization of the DFT matrix into a product of some specified matrices and lifting matrices. The elements of the lifting matrices are quantized to the nearest binary-number representation. Therefore, the proposed algorithm can be implemented in fixed-point arithmetic, using only shifting operations and additions. Any length-2(l) DFT sequence for l greater than or equal to 1 can be computed using this algorithm.

The design methodology of a multiplierless predictor is presented for differential pulse code modulation (DPCM) of images. This is a vital part of an image restoration and compression system. Multiplierless implies that each coefficient of the predictor is a power-of-2 number. Therefore, all multiplications can be performed by simple shifting operations. The predictor is designed as a two-dimensional (2-D) IIR filter with periodic coefficients. Simulation results illustrate the efficiency of the proposed predictor in the DPCM of images.

The design methodology of a multiplierless predictor is presented for differential pulse code modulation (DPCM) of images. Multiplierless implies that each coefficient of the predictor is a power-of-two number. Therefore, all multiplications can be performed by simple shifting operations. The predictor is designed as a two-dimensional (2-D) HR filter with periodic coefficients. Simulation results illustrate the efficiency of the proposed predictor in the DPCM of images.

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters is considered. The considered system is represented in state space by the first model of Fornasini-Marchesini (FM) with periodic coefficients. The stability of this model is then studied. Two necessary conditions and two sufficient conditions are established for asymptotic stability. The conditions are easy to use and computationally simple.

When digital filters are designed with power-of-two coefficients, the multiplications can be implemented by simple shifting operations. In this paper, the genetic algorithm (GA) is used to design 2D multiplierless filters. The 2D filter is designed to have periodically shift variant (PSV) coefficients. This increases the degrees of freedom for the multiplierless coefficients so that a better approximation can be achieved. The design involves finding the impulse response of the 2D PSV filter in closed form and then using the GA to find the filter coefficients. Two different types of GA are used, namely, the Binary-GA and the Integer-GA. Some design examples are presented to illustrate the concepts.

Hyperspectral images consist of the same image taken in different spectral bands. These images exhibit high correlation between the pixels in both the spatial and spectral dimensions. It is desirable to design a filter that takes advantage of this property. We implement an image restoration system and a coding system using a multidimensional filter. The image restoration system restores the lost samples and removes the additive noise using the least mean square (LMS) algorithm. For hyperspectral image coding, we use adaptive differential pulse code modulation (ADPCM) to achieve high compression of the image cube. Experimental results are very promising and illustrate the performance of the multidimensional filter.

This paper presents a new approach for restoring noisy images with a substantial number of missing samples. The system proposed is based on the linear prediction theory. The filters used are multiplierless since they have power-of-2 coefficients. This makes the algorithms fast and low cost for VLSI implementation. The system is composed of two stages. In the first one, the lost samples are recovered using the Least Mean Square (LMS)-like algorithm in which the missing samples are replaced by their estimates. In the second phase, noise is removed from the image using a genetic algorithm based linear predictor. This algorithm yields power-of-2 coefficients of the filter. The results are very promising and illustrate the performance of the multiplierless system.

The stability of periodically shift variant (PSV) filters are studied when implemented with two's complement truncation (TCT) quantization. Block form and standard (nonblock) form implementations are considered, and two sufficient conditions are established for stability. As a special case, second-order coupled-form PSV filters are then investigated under TCT quantization. Stability regions are established within the parameter space for block implementations. Examples are given to illustrate the results.

The stability of two-dimensional (2-D) periodically shift varying (PSV) filters formulated as the Givone-Roesser (GR) model is considered. The GR model is embedded into the 2(nd) model of Fornasini-Marchesisni (FM) and the stability of this embedded model is then studied. Several sufficient conditions and one necessary condition are obtained.

When digital filters are designed with power-of-2 coefficients, the multiplications can be implemented by simple shifting operations. For VLSI implementations, multiplierless filters are faster and more compact than filters with multipliers. In this paper, an algorithm for finding and updating the power-of-2 coefficients of an adaptive filter is designed. The new method uses the well-known Genetic Algorithm (GA) for this purpose. The GA is used in a unique way in order to reduce computations. Small blocks of data are used for the GA and only one new generation is produced per sample of data. This, coupled with the fact that the coefficients are power-of-2, yields a computational complexity of O (N) additions and no multiplications. The algorithm is investigated for applications in adaptive linear prediction and system identification. The results are very promising and illustrate the performance of the new algorithm. (C) 2002 Elsevier Science (USA).

A new least-squares adaptive algorithm, called the Euclidean Direction Search (EDS) algorithm is investigated for applications in fast adaptive filtering. Based on mathematical analysis and computer simulations, the proposed algorithm is shown to be very efficient for adaptive filtering applications such as noise cancellation and channel equalization. The algorithm features an O(N) computational complexity, fast convergence, improved numerical stability and least-squares optimal solution. Its convergence rate is comparable to that of the RLS but at a much lower computational cost

This paper presents a new approach for channel equalization using a multiplier-free adaptive algorithm. The algorithm is based on a quantized version of the Euclidean direction search method of optimization. The algorithm yields filter coefficients that are powers of 2, so that multiplications are reduced to simple shifts. The update equation for the coefficients is also multiplier-free. Computer simulations are given to illustrate the performance of the algorithm.